Control for Schrödinger operators on 2-tori: rough potentials

  • Jean Bourgain

    Institute for Advanced Study, Princeton, United States
  • Nicolas Burq

    Université Paris-Sud, Orsay, France
  • Maciej Zworski

    University of California, Berkeley, USA

Abstract

For the Schrödinger equation, on a torus, an arbitrary non-empty open set provides control and observability of the solution: . We show that the same result remains true for where , and is a (rational or irrational) torus. That extends the results of [1], and [8] where the observability was proved for and conjectured for . The higher dimensional generalization remains open for

Cite this article

Jean Bourgain, Nicolas Burq, Maciej Zworski, Control for Schrödinger operators on 2-tori: rough potentials. J. Eur. Math. Soc. 15 (2013), no. 5, pp. 1597–1628

DOI 10.4171/JEMS/399